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31.
A. M. W. Verhagen 《Journal of statistical physics》1976,15(3):219-231
An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given. 相似文献
32.
Davide Baccherini 《Discrete Mathematics》2008,308(18):4165-4176
We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion. 相似文献
33.
本文针对汽车保险中多车辆相撞事故的理赔建立起广义泊松过程模型,利用概率母泛函给出了其理赔总量在(0,t]内的均值与方差,并基于鞅分析方法证明了其破产概率的Lundberg不等式. 相似文献
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In this paper we give new and purely analytical proofs of a number of classical results on the asymptotic behavior of large random matrices of complex Wigner type (the GUE-case) or of complex Wishart type: Wigner's semi-circle law, the Harer-Zagier recursion formula, the Marchenko-Pastur law, the Geman-Silverstein results on the largest and smallest eigenvalues and other related results. Our approach is based on the derivation of explicit formulae for the moment generating functions for random matrices of the two considered types. 相似文献
38.
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values. 相似文献
39.
Hans J. Weber 《Central European Journal of Mathematics》2007,5(3):581-595
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given. 相似文献
40.
An urn has balls of colors C1 and C2. It is replenished (R) by balls of both colors and then depleted by (D) the same number; this constitutes a cycle. When R = D, the system is closed and equilibrium will be reached after many cycles. The ultimate distribution is found only when the replenishment is the same for each color. Asymptotic normal and asymptotic binomial distributions arise when the parameters reach extreme values. For the multicolor urn an expression is given for the correlation between the number of balls of any two colors. 相似文献